Added log-domain summation

appengine/findit/libs/math/test/logarithms_test.py

+# Copyright 2016 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
+import unittest
+
+from libs.math.logarithms import logsumexp
+
+
+INFINITY = float('inf')
+
+
+class LogarithmsTest(unittest.TestCase):
+
+  def testLogsumexpEmpty(self):

[inferno, 2016/12/04 23:51:24]

Can we have a test actual value for logsumpexp for simple inputs ? 
Also, a test that shows different results from math.log(math.fsum(math.exp(x)
for x in xs))) ?

[wrengr, 2016/12/05 19:12:59]

Testing concrete values is problematic because the result will be platform &
Python-version dependent, and therefore flaky. Showing the result is different
from the naive implementation will be similarly flaky for any interesting (i.e.,
borderline) values, but I can come up with some non-flaky examples where the
naive thing always over-/underflows, if desired.

+    """The empty sum is zero, log of zero is negative infinity."""
+    self.assertEqual(-INFINITY, logsumexp([]))
+
+  def testLogsumexpInfinite(self):
+    """If any summand is infinite, the whole thing is infinite."""
+    self.assertEqual(INFINITY, logsumexp([INFINITY]))
+    self.assertEqual(INFINITY, logsumexp([INFINITY, -INFINITY]))
+    self.assertEqual(INFINITY, logsumexp([0, 1, 2, INFINITY, 9, 8, 7]))
+
+  def testLogsumexpCommutative(self):
+    """Check that ``log(x+y) == log(y+x)`` as it should."""
+    # N.B., we must choose these two values carefully, to ensure we
+    # don't trivially pass the test.
+    xs = [0.1, 0.3]
+    ys = xs[::-1]
+    self.assertEqual(logsumexp(xs), logsumexp(ys))